People really are naïve. Normal people cannot comprehend at gut level that others can be as evil as what the terrorists do. They just can't. Until it happens to them. Even then they tend to downplay it as an isolated incident.
What people don't understand is that there is no way of ensuring what an immigrant's/refugee's purpose is for coming here. They aren't going to reveal how they really feel about our society if they know it will keep them out.
Families who come here secretly hating our western civilization can raise their children to harbour the same hatred, grow up and commit terrorist acts. Attitudes get handed down from generation to generation.
When this happens, of course the conclusion is that the kids were 'radicalized' here by some outside influence.
When actually, they were 'radicalized' from birth by their own families.